Model-dependent forest stand-level inference with and without estimates of stand-effects

Forest stands are important units of management. A stand-by-stand estimation of the mean and variance of an attribute of interest (Y) remains a priority in forest enterprise inventories. The advent of powerful and cost effective remotely sensed auxiliary variables (X) correlated with Y means that a census of X in the forest enterprise is increasingly available. In combination with a probability sample of Y, the census affords a model-dependent stand-level inference. It is important, however, that the sampling design affords an estimation of possible stand-effects in the model linking X to Y. We demonstrate, with simulated data, that failing to quantify non-zero stand-effects in the intercept of a linear population-level model can lead to a serious underestimation of the uncertainty in a model-dependent estimate of a stand mean, and by extension a confidence interval with poor coverage. We also provide an approximation to the variance of stand-effects in an intercept for the case when a sampling design does not afford estimation. Furthermore, we propose a method to correct a potential negative bias in an estimate of the variance of stand-effects when a sampling design prescribes few stands with small within-stand sample sizes.